However, whereas Suber is a professional academic, I am not. Before reading any further, read my disclaimer and warning on my My Writings page.
Identity, Constitution, and Statues made of Clay
Glenn Mason-Riseborough (12/10/2002)
I Background
Here is a problem. Let’s imagine a situation; let’s call it situation 1. An artisan makes a statue of a person out of clay. The artisan’s method is to make the statue in two pieces. He appropriately shapes each piece individually, and then sticks the two pieces together. The presumption is that (1) the statue does not exist prior to the two pieces being stuck together, and comes into existence the moment the two pieces are stuck together, (2) the lump of clay, from which the statue was made, does not exist prior to the two pieces being stuck together, and comes into existence the moment the two pieces are stuck together, and hence (3) the statue and the lump of clay both come into existence at the same time. The story then goes that the artisan, being frustrated with the artistry, puts the work—the entire statue made of clay—in a chemical solvent that dissolves the work. Again, the presumption is that both the statue and the lump of clay cease to exist at the same time. The statue and the lump of clay come into existence at exactly the same time; the statue and the lump of clay cease to exist at exactly the same time. The lump of clay constitutes the statue over the lifetime of both the lump of clay and the statue. Let’s imagine another situation; let’s call it situation 2. Another statue is created in exactly the same way as the statue in situation 1. But the artisan, presumably not quite as frustrated, decides merely to squash the statue (rather than dissolve it in solvent). Thus, while the statue ceases to exist at the moment it gets squashed, the lump of clay continues to exist for some indefinite period after the squashing. The statue and the lump of clay come into existence at exactly the same time; the statue and the lump of clay do not cease to exist at exactly the same time—the lump of clay outlives the statue. The lump of clay constitutes the statue until the squashing, but not after it. Let’s imagine yet another situation; let’s call it situation 3. Yet another statue is created in exactly the same way as the statues in situation 1 and situation 2. But the artisan, presumably less frustrated again, decides that instead of destroying the statue he will merely alter it. First, he dissolves the arms and calves of the statue in a solvent. Then he creates new arms and calves from a different piece of clay and attaches the new arms and calves to the statue. The presumption is that (1) the very same statue that exists before the arms and calves are dissolved continues existing through and after the dissolving and replacement, but (2) the lump of clay that exists before the dissolving does not continue existing after the dissolving, since some parts of the lump of clay have been removed through the dissolving. The statue and the lump of clay come into existence at exactly the same time; the statue and the lump of clay do not cease to exist at exactly the same time—the statue outlives the lump of clay. The lump of clay constitutes the statue until the dissolving, but not after it.
What is the problem? The problem is that this set of situations highlights a clash in intuitions, which many people possess. It seems that if we are going to develop a coherent theory about how to understand the metaphysics behind what is going on, then we will have to give up on a number of prima facie plausible intuitions. After all, a theory shouldn’t contain contradictory propositions. Whichever theory we adopt, there is going to be some unpleasantness, because it requires us to accept counter-intuitive claims (that is, deny certain intuitions). And there is disagreement about which intuitions are the most give-up-able. Coherent theories may nonetheless be implausible because they depart far too radically from common-sense intuitions. But common-sense for whom? Consequently, there is disagreement about the content of the theory we should adopt regarding the sort of entities present. What are some of these intuitions?
On the one hand, it seems clear to most people that in situations 2 and 3 the statue and the lump of clay hold different properties. In situation 2, not only does the lump of clay actually outlive the statue, but it also holds the property of surviving the squashing (and the additional property of being able to survive any squashing), which the statue does not. In situation 3, not only does the statue actually outlive the lump of clay, but it also holds the property of surviving the arm and calf replacements (and the additional property of being able to survive an arm and calf replacement), which the lump of clay does not. It also seems intuitively clear that for two things to be identical with each other, both must have exactly the same properties. If two objects have different properties, then they are different objects. This, simply put, is Leibniz’s Law. Hence, it seems plausible to say that, for situations 2 and 3, the statue is not identical with the lump of clay. This observation leads one to draw the further conclusion that, likewise, in situation 1 the statue and the lump of clay are not identical with each other. This is because while it is true that they actually temporally coincided exactly (came into existence and ceased to exist at exactly the same times as each other), they might not have. The statue can survive replacements, but the lump of clay can’t; the lump of clay can survive squashing, but the statue can’t. The statue could have survived certain events that the lump of clay would not have survived, and the lump of clay could have survived certain events that the statue would not have survived. In other words, the statue and the lump of clay hold different modal properties, and since they hold different properties, they must not be identical. Secondly, it seems plausible to say that identity is necessary. That is, whether or not two things are identical shouldn’t depend on some contingent fact, such as whether the artisan chooses to squash the statue or not. To many it seems intuitively mistaken to say that if the artisan had chosen to destroy the statue and the lump of clay in the solvent then the statue and the lump of clay are identical, but if the artisan had chosen to squash or alter the statue then the statue and the lump of clay are not identical. Surely the metaphysical fact of whether or not the statue and the lump of clay are identical should not depend on the whims of a frustrated artisan. And thus we should say that either the statue and the lump of clay are identical in all three situations, or they are not identical in any of the three situations; we ought not say they are identical in some of the situations but not others.
On the other hand, all of this clashes with another set of plausible intuitions. Firstly, it seems plausible to suggest that two distinct objects cannot be in the same place at the same time. In normal everyday thinking many people baulk at the idea that two distinct objects might exist in the same place at the same time and be made of exactly the same matter. And, since in all three situations the statue and the lump of clay are, for at least some of their respective lives, occupying the same space at the same time and are made up of exactly the same matter, the statue and the lump of clay in all three situations must be identical with each other. But supposing we could accept that sometimes two distinct objects can be in the same place at the same time and made up of the same matter (after all—and while this is not an identical situation it at least might soften us up—we usually accept that two houses that share a common wall are nonetheless distinct entities), there is another common intuition on this side. This is the thought that while two distinct objects may sometimes exactly coincide, they cannot exactly coincide at all times at which either exists. Since, in situation 1, the statue and the lump of clay came into existence at exactly the same time, ceased to exist at exactly the same time, were in the same place at the same time at all times while they both existed (exactly physically coinciding with each other), and made of exactly the same matter, with no remainder, the statue and the clay must be identical with each other. Another intuition is that, in everyday thinking, if we were to count the objects present, we would want to say that there is only one object, the statue/clay. We tell our children they are wrong if they say there are two objects. But it seems that if we don’t say that the statue and the lump of clay are identical, we would have to admit that there really are two objects present – one, the statue, and two, the lump of clay. In addition, a motivation for the intuition is the unpleasant thought that if we deny that the statue and the lump of clay are identical in situation 1, we are opening the door to the view that, for all we know, there are dozens of distinct objects exactly coinciding with any number of our common everyday objects, such as tables, trees or people. It opens the door to saying that there may be some other distinct objects (other than the person Glenn) exactly physically coinciding with me over my lifetime. Another motivation is the observation that, especially in situation 1, the statue and the lump of clay clearly do stand in some sort of intimate relationship with each other, and if it is not identity, then what it is? The answer, typically, is constitution (the lump of clay constitutes the statue), but what, exactly, does this mean?
The disagreement over the plausibility or implausibility of each of these sets of intuitions provides different jumping-off points for different metaphysicians writing on this topic. Mark Johnston,[1] in his paper “Constitution is not Identity,” apparently feels more comfortable with the first set of intuitions. On his first page he writes of it being “natural to conclude” in favour of non-identity, and writes that certain philosophers “go to some lengths to resist” it. In contrast, Harold W. Noonan,[2] in his reply to Johnston entitled “Constitution is Identity,” prefers the second set of intuitions. Noonan adopts a modus tollens positions when he writes “it is unclear, I think, why the fact that denying (CII) [constitution is identity] entails acknowledging that Goliath [the statue] is distinct from Lumpl [the lump of clay] should not, by itself, count as good reason for accepting it.”[3] In addition, Johnston cites David Lewis, Alan Gibbard, Anil Gupta and Denis Robinson as likewise defending a picture that sits most comfortably with the second set of intuitions.[4] But intuitions alone are not sufficient reason for holding a certain theory correct (especially if intuitions differ from person to person), and each of these writers develop arguments defending his view. These arguments have to show that:
(I) One’s own position is not self-contradictory,
(II) The counter-intuitive claims of one’s own position are really not so bad, and
(III) At best the opponent’s position is self-contradictory, but if the opponent’s position is not self-contradictory, then at the very least the counter-intuitive claims accepted by the opposition are really bad, or lead on to further really bad counter-intuitive positions.
In this essay I wish to examine some of these arguments, with the aim of deciding which position, if any, is the strongest, and consequently which set of intuitions is the most plausible to maintain. I will do this via an exposition and critical discussion of Johnston’s paper and Noonan’s reply. I will structure this by looking at some of the arguments given by Johnston and Noonan for their respective positions, and the replies that the other person gives, evaluating each argument as I go. Following Noonan, I will call his position, the thesis that constitution is identity, thesis (CII); following Johnston and Noonan (who follow Gibbard) I will call the statue Goliath and the lump of clay Lumpl. Johnston’s aim in his paper is to defend the anti-(CII) position (broadly, the first set of intuitions). He claims that (CII) is incoherent because Goliath and Lumpl have different modal properties, and this contradicts Leibniz’s Law. He also sets up what he sees as the strongest (CII) arguments, and argues that they all fail. And in this claimed failure Johnston attempts to show that one must reject (CII) if one is to reply adequately to the problem of the many. Johnston claims that (CII) fails on two counts: (a) because it is unable to reply to the charge of inconsistency, and (b) the problem of the many can only be solved if (CII) is rejected. Noonan’s main strategy is to show how Johnston’s arguments fail, and in so doing resurrect one of Johnston’s (CII) arguments, showing that, in fact, it works. He then provides two further arguments for (CII), one by looking at four-dimensionalist theories, and the other by showing how opponents of (CII) are forced to accept some very unpleasant consequences, to do with the existence of coincident, but distinct, entities. Noonan claims that (CII) turns out to be the preferable theory, because of these three main arguments for it. Due to space constraints I will not give an exhaustive treatment of all points considered, either in Johnston and Noonan or elsewhere. In particular I will not engage in any detailed discussion of four-dimensionalist arguments for the claim that constitution is identity, and will not discuss Noonan’s final argument for (CII) based on plausibility. Rather, I will focus on Johnston’s two arguments against (CII), and Noonan’s reformulation of Johnston’s second argument for (CII).
In the case of situation 1, Lumpl constitutes Goliath. But, as pointed out above, one of the main intuitions for holding that Lumpl is not identical with Goliath is the fact that they hold different modal properties. Those defending (CII) have to explain how it is consistent to say that, paraphrasing Johnston,
(1) For situation 1, Lumpl is identical with Goliath, while also saying that
(2) Lumpl can survive squashing but Goliath can’t; Goliath can survive replacement but Lumpl can’t.
Substituting (1) into (2) we get the apparently straightforward contradiction,
(3) Lumpl can survive squashing but Lumpl can’t; Lumpl can survive replacement but Lumpl can’t.
Unless we can show how (1) and (2) are consistent, and don’t result in a contradiction such as what appears to be the case with (3), (CII) must be rejected as contradictory. Johnston argues that (CII) defenders cannot adequately reply to this criticism, and Noonan argues that there is a way. What is Noonan’s way?
Noonan warms us up by introducing the concept of Abelardian predicates. An Abelardian predicate is, to quote Noonan, “a predicate whose reference (i.e. the property or (Fregean) concept denoted by it) can be affected by the subject term to which it is attached.”[5] Noonan gives an uncontroversial, non-modal, instance of an Abelardian predicate via an example from Willard Van Orman Quine. This is the predicate “was so-called because of his size.” Apparently, “Giorgione” was the nickname of Barbarelli—Barbarelli was a big guy, and “Giorgione” means large in Italian. Giorgione was so-called because of his size, but Barbarelli was not so-called because of his size. Even though we are talking about one and the same person (Giorgione is identical with Barbarelli), it matters a great deal which subject term (“Giorgione” or “Barbarelli”) we attach to the predicate “was so-called because of his size.” When attached to “Giorgione” the predicate refers to the property “being called ‘Giorgione’ because of his size;” when attached to “Barbarelli” the predicate refers to the property “being called ‘Barbarelli’ because of his size.” Changing the spelling of the singular term (“Giorgione” or “Barbarelli”) has changed the property to which the predicate refers. So far, so good. How does this relate to the case at hand?
Noonan states that those who defend (CII) must accept that modal predicates are Abelardian, and that this provides a way out of the apparent contradiction. That is, those who accept (CII) must accept that the reference of a predicate like “would not have been destroyed if squashed” may change depending on a component of the sense of the subject term used, such as “Lumpl” or “Goliath.” To give an example, Noonan cites Lewis’ counterpart theoretic view, which Noonan thinks is one possible fleshing out of the Abelardian nature of modal predicates (Noonan also names Gupta as providing another way of fleshing out how modal predicates are Abelardian, but does not elaborate). On Noonan’s interpretation of the Lewis view, very briefly, to determine the truth condition of the modal claim one picks out the relevant counterpart in other possible worlds. But the particular appropriate counterpart that we pick out is going to depend on whether we are thinking about a statue counterpart relation (invoked by “Goliath”) or a lump of clay counterpart relation (invoked by “Lumpl”). That is, it is determined, in part, by the sort of properties of the object (such as statue properties or lump-of-clay properties) that are picked out by a component of the sense of the subject term. The semantics of “Goliath” require us to pick out a statue counterpart, and the semantics of “Lumpl” require us to pick out a lump of clay counterpart.[6]
But let’s slow down a minute here. Is this really Lewis’ view? Robinson (in conversation) thinks probably not. Robinson thinks that Lewis’ view is probably slightly different from Noonan’s view, and is a more liberal way of understanding what is going on than Noonan’s view. But whatever the case about interpreting Lewis, Robinson thinks it is possible to strengthen the (CII) position by loosening up on the necessity for (CII) defenders to accept the contentious issue of modal predicates being Abelardian. In other words, Robinson argues that those who accept (CII) need not accept that modal predicates must be Abelardian—they have an alternative view that they might hold. Further, he suggests that this non-Abelardian account of modal predicates has greater explanatory power, and it is even more help to those wishing to defend (CII). The reasoning is as follows: Robinson uses the distinction between semantics and pragmatics. Semantics is the aspect of meaning and reference that does not vary between situations, and applies to all token-instances of a particular word. Pragmatics is the aspect of meaning and reference that varies from instance to instance of utterance. Examples of pragmatics include expressions which include words like “he,” “she,” “that,” etc., where it is the context that gives the words meaning (these words are typically called indexicals). To repeat, in the case of Noonan’s Abelardian predicates, it is semantics, not pragmatics, that do the work to give the meaning. “Lumpl,” as a rigid designator, corresponds to the indefinite description “a lump of clay.” On this account, part of what we mean by “Lumpl” is that Lumpl is a lump of clay. And so in all situations “Lumpl” invokes the lump of clay counterpart relation (never the statue counterpart relation). Hence, there is a fact of the matter about, for example, “Lumpl would not have been destroyed if squashed.” And the fact of the matter is that this is a true statement. In contrast, Robinson asks why we should not allow that, at the very least in some situations, pragmatics also plays a part in determining which counterpart relation should be invoked. Robinson suggests that modal predicates can have an indexical element to their meaning, and, depending on the context, the same predicate with the same singular term can refer to different properties. Thus, Robinson thinks that there will not be a fact of the matter about, for example, “Lumpl would not have been destroyed if squashed.” As shown above in the explanation of Abelardian predicates, it is clear that we would want to say in many contexts that the statement is true. Obviously this would be the dominant feature of “Lumpl,” but would we want to say it is true in all situations? Robinson thinks not. For example, someone might argue that:
(A) Goliath would have been destroyed if squashed,
(B) Lumpl is Goliath,
(C) Whatever is true of Goliath is also true of Lumpl, so
(D) Lumpl would have been destroyed if squashed.
And Robinson thinks that, in the context, since true claims about Goliath were made, we can say that “Lumpl would not have been destroyed if squashed” is a false statement. In this context “Lumpl” is invoking the statue counterpart relation, not the lump of clay counterpart relation. Thus in some situations “Lumpl would not have been destroyed if squashed” is true and in other situations it is false. It is the context (pragmatics) that determines how the claim should be interpreted, not just the semantics. And hence the modal predicate is not Abelardian, yet it still supports (CII). And Robinson sees accepting that, in some situations, there may be no fact of the matter independent of context as a strength. This pragmatics account of modal predicates is not denying that perhaps sometimes modal predicates are Abelardian, it is just not forcing the (CII) defender to hold that it is the case all the time. An even clearer advantage of a pragmatics approach over the Abelardian predicate approach is that it provides a strategy for understanding modal predicates that have no singular term. For example, the statement “the unique statue-shaped thing here made of clay would not have been destroyed if squashed” clearly relies on pragmatics to give it meaning to determine the truth condition. In some situations it can be said to be true (when pragmatics invokes the lump of clay counterpart relation), and in other situations it can be said to be false (when pragmatics invokes the statue counterpart relation), and it is context that determines whether it or its negation is true.
What does this mean in the context of the charge of inconsistency against (CII)? It means that there are two possible ways for the (CII) defender to reply to show that the apparent contradiction is really no contradiction at all. Firstly, on the Noonan position we can say that while (3) is contradictory, (1) and (2) don’t entail (3). The (CII) defender can accept both (1) and (2) without contradiction. S/he can do this by holding that modal predicates are Abelardian, and as such the sense of the singular terms gives the meaning. While the singular terms refer to the same object, they have different senses that invoke different counterpart relations, and so the predicates refer to different properties. Secondly, on the Robinson position one can allow that in some situations (1) and (2) entail (3), but that (3) is not really contradictory. This is because part of the meaning of the singular term is determined by context, and in some situations the singular term can invoke one counterpart relation, and in other situations the same singular term can invoke a different counterpart relation. And so, as with the Abelardian account, the predicates refer to different properties. So the (CII) defender has shown that the straightforward argument of contradiction fails. But Johnston has another argument against (CII), which he introduces via a reply to an argument for (CII). I turn to this now.
III A (CII) argument, and a reply which
has an anti-(CII) argument built in
Johnston states that he knows of only two arguments for (CII) that have any plausibility, but claims to show how both fail. Johnston’s first argument is an argument from mereology, which is the study of the part/whole relation. Noonan does not discuss Johnston’s first argument, and seems satisfied with Johnston’s reasoning as to why it fails. I will not discuss it either, and will instead focus on the second argument. In the case of the second argument, Johnston argues that the (CII) opponent’s reply to the argument puts the opponent of (CII) on the offensive. In his reply to the second argument, Johnston claims that it must be the case that constitution is never identity. Johnston puts forward his second argument for (CII) in section III, and rejects it in section IV. Central to this argument is (using Johnston’s numbering):
(8) If y is a paradigm F and x is intrinsically exactly like y then x is an F.
The argument is that if (8), or any suitable replacement of (8), is true, then we have a reductio ad absurdum of the claim that Goliath is not identical with Lumpl (i.e., an argument for (CII)). The argument is (paraphrasing Johnston):
(i) Suppose, by reductio, that Goliath and Lumpl are distinct.
(ii) Goliath is a paradigm statue of Goliath and Lumpl is intrinsically exactly like Goliath.
(iii) So, Lumpl is a statue of Goliath (from (ii) and (8)).
(iv) But, there are two problems:
(a) We have got (at least) two statues of Goliath (the extra statues come in because we might give the name “Lumpl*” to the piece of matter, or the collection of molecules, or the collection of atoms, or … which constitutes Lumpl, argue that Lumpl* is distinct from Lumpl and Goliath, and by (8) Lumpl* is a statue too).
(b) It turns out that Lumpl must have the modal properties of a statue, contra our original claim that lumps of clay do not hold the same modal properties as statues.
(v) So, Goliath and Lumpl cannot be distinct, and (CII) is true.
Johnston replies to this argument by claiming that (8) entails
(9) If y is a paradigm F and x is an entity that differs from y in any respect relevant to being an F only minutely then x is an F.
But (9) is false. So, by modus tollens, (8) must be false. And so the reason for holding that (iii) is true no longer holds, and the reductio fails to prove that (CII) is true. Why is (9) false? Johnston’s answer is that it has to do with Peter Unger’s “problem of the many.” What is the problem of the many? We observe:
(10) In the closest vicinity of any paradigm middle sized material F there are usually very many entities that differ only very minutely from the paradigm in any respect.
Unger’s example is that of a cloud, but we could give the same argument for any materially complex object. A cloud, c, consists of a dense cluster of water droplets and has a large number of water droplets surrounding it. In the closest vicinity of c there are many cloud-shaped clusters of water droplets, some of which may differ from c with respect to only one water droplet. Some clusters of water droplets will be proper parts of c, and c will be a proper part of other clusters of water droplets. But if (9) is true, then it is the case that in the closest vicinity of c there are very many, highly coincident, almost overlapping clouds. And, it is highly counter-intuitive to say that there are very many clouds in this way (Noonan goes so far as to say that it is simply false). Thus, to preserve our intuition, (9) must be false. And so the argument for (CII) fails, on the assumption that a (CII) theorist would not wish to accept that there are very many, highly coincident, almost overlapping clouds.
Johnston continues. He is not happy with Unger’s solution to the problem of the many, which Johnston calls Eliminative Nihilism. Whereas for Johnston clouds are not identical with the water droplets that constitute the clouds, yet clouds still exist, for Unger clouds do not really exist at all—all that exists is clusters of matter. That is, for Unger, the upshot of the problem of the many is that we must conclude that there are really no materially complex F’s for any sort F (no tables, trees, clouds, people, etc.). Johnston finds this consequence given by Unger unpalatable so attempts to give a better solution. At the very least Unger’s view departs extremely radically from common-sense intuitions, so presumably we should only use it as a last resort if we cannot find a solution that sits more comfortably with our intuitions. And further, in giving his better solution, Johnston aims to provide a positive argument against (CII).
Firstly, Johnston writes that the solution cannot be simply one of vagueness, where the problem of the many disappears once we provide an adequate treatment of the problem of vagueness. Rather, Johnston’s solution to the problem of the many is, unsurprisingly, the thesis that constitution is not identity. In this way, Johnston has constructed a positive argument against (CII) out of showing a failing in a positive argument for (CII). Johnston claims that the problem of the many disappears if we accept that none of the cloud-shaped clusters of water droplets in the closest vicinity of c are clouds, including any that might constitute clouds. All they are, are cloud-shaped clusters of water droplets. On the face of it, this solution would appear to be a better solution than Unger’s solution, since at least we retain the intuition that clouds, etc. really do exist. More formally, Johnston labels the large number of cloud-shaped clusters of water droplets k0, k1, k2, k3, …. Firstly, Johnston states that none of k0, k1, k2, k3, … are clouds—in other words none of k0, k1, k2, k3, … is identical with c. This is because none of k0, k1, k2, k3, … are of the right category to be clouds. Clouds belong to the category of material objects, and k0, k1, k2, k3, … belong to the category of matter that constitutes such material objects. Johnston modifies (9) and (8) to include this restriction:
(9’) If y is a paradigm F and x is an entity that differs from y in any respect relevant to being an F only minutely and x is of the right category, i.e. is not a mere quantity or piece of matter, then x is an F.
(8’) If y is a paradigm F and x is intrinsically exactly like y and x is of the right category, i.e. is not a mere quantity or piece of matter, then x is an F.
And accepting that (8’) is true (and (8) is not true), does not give us any grounds for accepting that (iii) is true, because Lumpl is not of the right category to be a statue.
Secondly, Johnston states that none of k0, k1, k2, k3, … definitely constitute c. This is because Johnston thinks that the problem of the many has shown us that constitution is a vague relation. There is no good reason for choosing one sharpening over another, and rather than choose arbitrarily (or deny the existence of clouds altogether like Unger) we should accept that there is no fact of the matter about which sharpening is the correct one. We may legitimately sharpen c in any number of different ways—on one sharpening k0 constitutes c, on another sharpening k1 constitutes c, on yet another sharpening k2 constitutes c, and so on.
Noonan responds to Johnston’s argument in section II of his paper. He claims that, contrary to Johnston, the argument for (CII) does work, and Johnston’s argument for the rejection of (CII) fails.
Firstly, discussing Noonan’s reasons for arguing that Johnston’s argument for the rejection of (CII) on the basis of the problem of the many fails. Noonan writes that, for Johnston’s argument to work, his reply to the problem of the many must be the only possible solution, and not one solution among many. This is not quite right and Noonan appears to slightly exaggerate. For Johnston’s argument to work, his solution must be better than any competing solution that either denies that constitution is not identity, or is neutral on this issue. That is, Johnston’s argument still could work if there are other solutions, as long as all the other solutions either require that constitution is not identity, or have higher prices to pay in terms of entailing more counter-intuitive claims than Johnston’s position. So, the defender of (CII) has to show that (a) Johnston’s position pays an extremely high price, and (b) there are other solutions that don’t require rejecting (CII) and don’t have such a high price. To the high price, first. Johnston acknowledges that on his account there is no fact of the matter about which sharpening of c is the correct sharpening. We could either interpret this as saying that there is linguistic vagueness, or c is a vague object. If we take the former option, then we could label each sharpening of c c0, c1, c2, c3, …, where cn is constituted by kn and cn is of the right category to be a cloud. But then the problem of the many comes back, as (9’) solved the problem by relying on there being a category distinction. Taking the latter option, that objects are vague, is a very high price to pay, in Noonan’s view (though presumably it is not as high as Unger’s solution). The next step for Noonan is to provide another solution that does not have such a high price. Noonan attempts to give two solutions. The first solution is to deny that we should count by identity, and that we should instead count by constitution. We say that we only count once some object and some proper part of that object. If k1 is a proper part of k0 then we only count it once. Where “Tibbles” is a cat and “Tib” is the cat excluding its tail, we would only count one cat. This might work for proper parts, but what about cases of partial overlap? This solution, as articulated, does not deal with this complication. In the case of two houses sharing the same wall we would intuitively want to count two houses. And if we wanted to conserve consistency with respect to this intuition, the problem of the many raises its ugly head again with respect to partially overlapping clusters of water droplets. Thus, it may turn out that this solution has a higher price to pay than Johnston’s solution. More work would need to be done to show which solution conserves intuitions better. Noonan’s second solution to the problem of the many attempts to deal with this complication. Noonan suggests:
(11) For any x and y, if x is a cloud and y is a cloud and x is highly coincident with y then x is identical with y.
Presumably, Noonan is not meaning to suggest here that two highly coincident, but not completely coincident clouds are one and the same cloud. This would be to suggest that a particular cloud might have, at one time, the property of being constituted by two different numbers of water droplets. Rather Noonan clarifies that any one of k0, k1, k2, k3, … might be a cloud under some sharpening, but no two could be clouds under the same sharpening. This is a solution that, like Johnston’s solution, has the consequence of vagueness. But, in this case, we can accept that the vagueness may be linguistic, and not in the object, since accepting linguistic vagueness does not regenerate the problem of the many in this situation. As such, this would appear to be the preferable theory, since these consequences identified are not so counter-intuitive.
So, what we have is at least four solutions to the problem of the many. For Johnston’s argument against (CII) to work he has to show that his is the best solution, since holding any of the other three doesn’t commit us to rejecting (CII). In this context the burden of proof is on Johnston, since this is a positive argument that (CII) is false. It seems to me that Noonan has done enough work to put doubt on Johnston’s argument (especially with his second solution), and Johnston needs to do more work to show how his solution has the fewer (and less) counter-intuitive consequences.
Turning now to the positive argument for (CII). As shown above, Johnston argues that it fails to prove (CII) because (8) is false. Noonan gives a two-fold reply. First he says that of course (8) is false, and it is false for at least two other reasons, independently of the problem of the many. Second he says that (8) can be modified and the argument for (CII) can be made to work, after all. Noonan’s first reason for rejecting (8) is that it ignores the requirement that for x to be an F it must have the correct causal origin. A rock carved by wind and water that resembles a face is not a statue (or more generally an artefact), because it was not carved by an intentional agent; Swampman (as it is usually argued) is not a person because it has no causal history (and on the Ruth Millikan account hence has no propositional attitudes). Noonan’s second reason is that it does not take into account proper parts—a proper part of a statue is not a statue, even if the proper part is intrinsically exactly like some other paradigm statue. For example, suppose there is a statue of a person, but with its arms destroyed. Suppose also that someone decides to craft a replica of the statue, as it was before the arms were destroyed. A proper part of the replica is the replica minus the arms. This proper part of the replica is intrinsically exactly like the original in its current state (which is a statue), but is not, itself, a statue. So, accepting that there are (at least) three reasons why (8) is false, Noonan attempts to propose a modified form of (8) and (9) such that (a) the modified (8) (with (ii)) logically entails (iii), and (b) both the modified forms of (8) and (9) are true. If both these criteria are satisfied, then the reductio argument (i) – (v) succeeds to show (CII). The modified (8) and (9) are (with the causal origin requirement taken as read):
(8*) If y is a paradigm F and x is intrinsically exactly like y and x does not partly overlap any F then x is an F.
(9*) If y is a paradigm F and x is an entity that differs from y in any respect relevant to being an F only minutely and x does not partly overlap any F then x is an F.
Does Noonan’s resurrected argument for (CII) succeed? Firstly, it is the case that (8*) does (with (ii)) logically entail (iii). Lumpl does not partly overlap any statue of Goliath, so the addition to (8) does not weaken (iii). Secondly, none of the three arguments that show (8) to be false show (8*) to be false. This is because (a) the causal origin requirement is trivially taken as read, (b) the modification explicitly excludes any situations where there is any overlap, so excludes proper parts of statues being statues themselves, and (c) again since partial overlap is excluded, we do not arrive at the problem of the many. Thirdly, and finally, I am not aware of any other arguments to show that (8*) is false.
Finally, presumably just in case the reductio argument above for (CII) fails, Noonan proceeds to give two further arguments for (CII), in section III and IV respectively. The first of these is an argument that, assuming that a four-dimensionalist metaphysic trivially entails (CII), attempts to prove a four-dimensionalist metaphysic independently of (CII). The second of these attempts to show that (CII) is the preferable theory, because its rejection entails an extremely bad counter-intuitive consequence. The counter-intuitive consequence, according to Noonan, is that of excessive ontological inflation—that is, we must accept a greater number of distinct entities than intuition would ordinarily suggest. This is back to the problem of the many again, which Noonan claims Johnston’s solution above fails to deal with, with respect to objects of the same category. I will note these two arguments, but will not discuss them any further here.
In this essay I have looked at two arguments given by Johnston for the thesis that constitution is not identity, and have shown that both fail. The first argument, that of the straightforward argument of contradiction based on modal predicates (discussed in section II above), is shown to fail if we take modal predicates to be either Abelardian or ambiguous. The second argument, that of rejecting (CII) in order to reply adequately to the problem of the many (discussed in section III above), fails because there are other possible replies to the problem of the many that are preferable or equally preferable. I have briefly discussed two possible replies given by Noonan (in addition to the reply by Johnston and the reply by Unger), one of which I suggest is the most plausible of the four solutions. But I don’t pretend to have given an exhaustive discussion of the problem of the many, and more work would need to be done (and has been done, which I haven’t considered here) to show which is the better solution. But for my purposes here, enough work has been done to show that, as it stands, replying to the problem of the many does not require rejecting (CII), and hence the argument fails. In this essay I have also looked at one argument for the thesis that constitution is identity (discussed in section III above). This is the argument given and rejected by Johnston, but revised and endorsed by Noonan. I have argues that, in fact, Noonan’s revised version of the argument succeeds, in as much as I am not aware of any arguments against it. Thus, on the basis of these three arguments discussed, and with the proviso that my examination is not exhaustive, as I see it, the weight of evidence is in favour of accepting that constitution is identity.
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Bibliography
Johnston, M. (1992). Constitution is Not Identity. Mind, 101(401), 89-105.
Noonan, H. W. (1991). Indeterminate Identity, Contingent Identity and Abelardian Predicates. The Philosophical Quarterly, 41(163), 183-193.
_____. (1993). Constitution is Identity. Mind, 102(405), 133-146.
Robinson, D. (1985). Can Amoebae Divide Without Multiplying? Australasian Journal of Philosophy, 63(3), 299-319.
Thomson, J. J. (1998). The Statue and the Clay. Noûs, 32(2), 149-173.
[1] Johnston, 1992.
[2] Noonan, 1993.
[3] Noonan, 1993, p. 135.
[4] Though Robinson rejects certain of these intuitions to do with counting in “Can amoebae divide without multiplying” (Robinson, 1985).
[5] Noonan, 1993, p. 134.
[6] See for example Noonan (1991) for further discussion on Abelardian predicates.